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A195097 Fractalization of (1+[3n/4]), where [ ] = floor.

%I A195097 #5 Mar 30 2012 18:57:44
%S A195097 1,1,2,1,2,3,1,2,3,4,1,2,3,5,4,1,2,3,5,6,4,1,2,3,5,6,7,4,1,2,3,5,6,7,
%T A195097 8,4,1,2,3,5,6,7,9,8,4,1,2,3,5,6,7,9,10,8,4,1,2,3,5,6,7,9,10,11,8,4,1,
%U A195097 2,3,5,6,7,9,10,11,12,8,4,1,2,3,5,6,7,9,10,11,13,12,8,4,1,2,3
%N A195097 Fractalization of (1+[3n/4]), where [ ] = floor.
%C A195097 See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence.  The sequence (1+[3n/4]) is a subsequence ofy A037915.
%t A195097 r = 3/4; p[n_] := 1 + Floor[n*r] (* A037915 *)
%t A195097 Table[p[n], {n, 1, 90}]
%t A195097 g[1] = {1}; g[n_] := Insert[g[n - 1], n, p[n]]
%t A195097 f[1] = g[1]; f[n_] := Join[f[n - 1], g[n]]
%t A195097 f[20]    (* A195097 *)
%t A195097 row[n_] := Position[f[30], n];
%t A195097 u = TableForm[Table[row[n], {n, 1, 5}]]
%t A195097 v[n_, k_] := Part[row[n], k];
%t A195097 w = Flatten[Table[v[k, n - k + 1], {n, 1, 13},
%t A195097 {k, 1, n}]](* A195098 *)
%t A195097 q[n_] := Position[w, n]; Flatten[Table[q[n],
%t A195097 {n, 1, 80}]](* A195099 *)
%Y A195097 Cf. A194959, A002265, A195098, A195099.
%K A195097 nonn
%O A195097 1,3
%A A195097 _Clark Kimberling_, Sep 08 2011